Quantitative Methods 【Reading 9】Sample statements, following, normal

cross-ied

Which of the following statements about the normal probability distribution is most accurate?

A) Five percent of the normal curve probability is more than two standard deviations from the mean.

B) Sixty-eight percent of the area under the normal curve falls between the mean and 1 standard deviation above the mean.

C) The normal curve is asymmetrical about its mean.

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The normal curve is symmetrical about its mean with 34% of the area under the normal curve falling between the mean and one standard deviation above the mean. Ninety-five percent of the normal curve is within two standard deviations of the mean, so five percent of the normal curve falls outside two standard deviations from the mean.

terpsichorefan

thanks for sharing

cyber21

A drawback of historical simulation is it:

A) depends on the accuracy of the random number generator.

B) may not accurately reflect possible outcomes.

C) may not account for very rare events.

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There are two major problems with historical simulation. The first is that it cannot account for events that do not occur in the sample. If a security began trading after 1987, for example, there would be no evidence of its behavior in a market crash. The other drawback is that the analyst cannot change the parameters of the distribution to examine how small changes might affect the asset’s behavior.

cyber21

The difference between a Monte Carlo simulation and a historical simulation is that a historical simulation uses randomly selected variables from past distributions, while a Monte Carlo simulation:

A) projects variables based on a priori principles.

B) uses randomly selected variables from future distributions.

C) uses a computer to generate random variables.

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A Monte Carlo simulation uses a computer to generate random variables from specified distributions.

cyber21

Many analysts prefer to use Monte Carlo simulation rather than historical simulation because:

A) computers can manipulate theoretical data much more quickly than historical data.

B) past distributions cannot address changes in correlations or events that have not happened before.

C) it is much easier to generate the required variables.

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While the past is often a good predictor of the future, simulations based on past distributions are limited to reflecting changes and events that actually occurred. Monte Carlo simulation can be used to model based on parameters that are not limited to past experience.

cyber21

Joan Biggs, CFA, acquires a large database of past returns on a variety of assets. Biggs then draws random samples of sets of returns from the database and analyzes the resulting distributions. Biggs is engaging in:

A) Monte Carlo simulation.

B) historical simulation.

C) discrete analysis.

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This is a typical example of historical simulation.

cyber21

Which of the following would least likely be categorized as a multivariate distribution?

A) The return of a stock and the return of the DJIA.

B) The days a stock traded and the days it did not trade.

C) The returns of the stocks in the DJIA.

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The number of days a stock traded and did not trade describes only one random variable. Both of the other cases involve two or more random variables.

cyber21

A multivariate normal distribution that includes three random variables can be completely described by the means and variances of each of the random variables and the:

A) correlation coefficient of the three random variables.

B) conditional probabilities among the three random variables.

C) correlations between each pair of random variables.

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A multivariate normal distribution that includes three random variables can be completely described by the means and variances of each of the random variables and the correlations between each pair of random variables. Correlation measures the strength of the linear relationship between two random variables (thus, "the correlation coefficient of the three random variables" is inaccurate).

cyber21

In a multivariate normal distribution, a correlation tells the:

A) relationship between the means and variances of the variables.

B) overall relationship between all the variables.

C) strength of the linear relationship between two of the variables.

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This is true by definition. The correlation only applies to two variables at a time.

cyber21

A multivariate distribution is best defined as describing the behavior of:

A) two or more independent random variables.

B) a random variable with more than two possible outcomes.

C) two or more dependent random variables.

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A multivariate distribution describes the relationships between two or more random variables, when the behavior of each random variable is dependent on the others in some way.